The most common and most likely answer to this crossword clue is the 10 letter word CHESSBOARD
I've seen this crossword clue in Financial Times
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More clues leading to the result CHESSBOARD
Buddy explains!
The straight part
We know that "On which a knight might attack a castle" is the straight/definition part of the clue. The straight part is often a synonym or definition, in this case on which a knight might attack a castle = chessboard.The cryptic/wordplay part
In cryptic crossword there's often an wordplay/cryptic part as well.This part involves a more complex hint, such as an anagram, homophone, hidden word, etc.
Sadly, We don't have an explanation for this specific crossword clue yet.
What does CHESSBOARD mean?
CHESSBOARD noun- The square board used in the game of chess, subdivided into eight rows of eight squares each, the squares in each row and column being of alternating colours.
- A mathematical construction based on this pattern of squares